Bound states in the continuum in symmetric and asymmetric photonic crystal slabs

Abstract

We develop a semi-analytical model to describe bound states in the continuum (BICs) in photonic crystal slabs. We model leaky modes supported by photonic crystal slabs as a transverse Fabry-Perot resonance composed of a few propagative Bloch waves bouncing back and forth vertically inside the slab. This multimode Fabry-Perot model accurately predicts the existence of BICs and their positions in the parameter space. We show that, regardless of the slab thickness, BICs cannot exist below a cut-off frequency, which is related to the existence of the second-order Bloch wave in the photonic crystal. Thanks to the semi-analyticity of the model, we investigate the dynamics of BICs with the slab thickness in symmetric and asymmetric photonic crystal slabs. We evidence that the symmetry-protected BICs that exist in symmetric structures at the Γ-point of the dispersion diagram can still exist when the horizontal mirror symmetry is broken, but only for particular values of the slab thickness.

Exploring the Optical Bound State in the Continuum in a Dielectric Grating Coupled Plasmonic Hybrid System

“…We have adopted the previously established theoretical frameworks [46,50,51] to understand the reflection characteristics of the HCG. Following the multimode Fabry-Perot model, [46,51] each diffracted plane wave in the high index slab can be contemplated as a Bloch mode satisfying the F-P cavity resonance condition for a selected slab thickness. In a broad sense, the hybrid geometry is identical to a cavity sandwiched between two mirrors that supports many F-P cavity modes.…”

“…The grating parameters are consistent with that of the grating constituent of the hybrid structure with F = 0.43. We have adopted the previously established theoretical frameworks [ 46,50,51 ] to understand the reflection characteristics of the HCG. Following the multimode Fabry–Perot model, [ 46,51 ] each diffracted plane wave in the high index slab can be contemplated as a Bloch mode satisfying the F–P cavity resonance condition for a selected slab thickness.…”

“…The existence of BICs and their location are generally explored by rigorous numerical methods with the help of cumbersome analysis based on coupled‐wave theory. [ 46 ] As the “finite‐difference time‐domain (FDTD)” based analysis can be convenient to study the interference effect and the bound state formalism, [ 19 ] we in our examinations have also employed the FDTD method to inspect the optical response of the fabricated hybrid geometry. For a better understanding of the nature and origination of the resonant modes in the proposed hybrid geometry, we have initially selected a simple rectangular grating profile with a low fill fraction to investigate and classify its supported modes.…”

Accidental and symmetry-protected bound states in the continuum in a photonic-crystal slab: A resonant-state expansion study

“…Ideally, BICs have an infinite Q factor, corresponding to δ-like features in optical spectra and infinitely long lifetimes, and therefore have found applications in lasers [20,21], sensing [22], and filtering [23]. In periodic optical systems and in particular PC slabs, BICs have become the subject of growing theoretical interest in recent years [24][25][26][27][28], including development of various perturbative approaches [29][30][31][32][33][34][35][36] and other approximate methods [37,38].…”

“…Compared to this model, the RSE takes into account all possible channels and basis modes within each channel, striving towards the exact solution. Another recent paper [38] studying BICs in PC slabs uses instead the modes of an infinite PC as basis for treating a finite PC slab. The semianalytic model developed in that paper also neglects any evanescent solutions and in practice presents a reduced version of the rigourous scattering-matrix method [9,10].…”